DC MAGNETOTRANSPORT AND HALL-EFFECT IN MULTIPLY CONNECTED QUANTUM-WIRE SYSTEMS

In the Landauer-Buttiker approach, the dc-transport properties of a sy stem are expressed in terms of its scattering matrix. We propose a met hod to sum the multiple-scattering events for an arbitrary ensemble of interconnected scatterers, which leads to a closed analytic expressio n for the matrix elements of the overall-scattering matrix. This appro ach is used to investigate the dc magnetotransport of a planar periodi c lattice of interconnected quantum wires. The calculated conductance as well as the Hall voltage depend strongly on the Fermi wave vector a nd on the magnetic field. This behavior is a consequence of the interf erence between waves traveling along different scattering paths. It is closely related to the eigenvalue spectrum of electrons in a two-dime nsional lattice in the presence of a perpendicular magnetic field, whi ch is described by the Hofstadter butterfly. We present a detailed ana lysis of the observed features of the Hall voltage.